CAMP (Computational, Applied Mathematics and PDE) Seminar

The seminar meets regularly on Wednesdays at 4pm in Eckhart 202. We also have special seminars during other days. This quarter the seminar will be running remotely via zoom. Access to the zoom links will be provided via the email list. To subscribe or unsubscribe from the email list, you may either go to Camp/PDE email list or contact Cornelia Mihaila.

Spring 2021 Schedule.

May 5
Brian Seguin, Loyola Univeristy, Chicago Online, 4pm.
Nonlocal Curvature of Surfaces and Curves
Motivated by generalizations of the Ginsburg-Landau energy and the diffusion equation in which derivatives are replaced by fractional derivatives, Caffarelli, Roquejoffre, and Savin studied the minimizers of a fractional perimeter functional on sets involving a fractional parameter. Such minimizers have to satisfy a pointwise condition on their boundary, which can be used to define a notion of nonlocal mean-curvature. This definition only holds for surfaces which are the boundary of a set. I will describe how to define a nonlocal notion of mean-curvature for any surface by introducing a fractional area functional and considering its minimizers. Moreover, I will describe how these ideas can be extended to curves by defining a fractional length and an associated nonlocal curvature for a curve.

For questions, contact Cornelia Mihaila at: cmihaila [at] math [dot] uchicago [dot] edu.

Previous quarters:

Winter 2021 Fall 2020 Spring 2020 Winter 2020 Fall 2019 Spring 2019 Winter 2019 Fall 2018 Spring 2018 Winter 2018 Fall 2017 Spring 2017 Winter 2017 Fall 2016 Spring 2016 Winter 2016 Fall 2015 Spring 2015 Winter 2015 Fall 2014 Spring 2014 Winter 2014 Fall 2013 Spring 2013 Winter 2013 Fall 2012 Spring 2012 Winter 2012 Fall 2011 Spring 2011 Winter 2011 Fall 2010 Spring 2010 Winter 2010 Fall 2009 Spring 2009